LMFDB - Embedded newform 100.9.f.c.57.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [100,9,Mod(57,100)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("100.57"); S:= CuspForms(chi, 9); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(100, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 9, names="a")

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	100.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$40.7378610061$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 8 x^{10} + 1412 x^{9} + 550393 x^{8} - 1456736 x^{7} + 2420672 x^{6} + \cdots + 547748010000 $ x^12 - 4x^11 + 8x^10 + 1412x^9 + 550393x^8 - 1456736x^7 + 2420672x^6 + 375321568x^5 + 69558134536x^4 - 89027503680x^3 + 58317955200x^2 + 252758952000*x + 547748010000
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{22}\cdot 3^{6}\cdot 5^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			57.3
Root			$-0.905864 + 0.905864i$ of defining polynomial
Character	$\chi$	$=$	100.57
Dual form			100.9.f.c.93.3

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-11.9100 + 11.9100i) q^{3} +(-2673.78 - 2673.78i) q^{7} +6277.30i q^{9} -8327.31 q^{11} +(1552.39 - 1552.39i) q^{13} +(39830.2 + 39830.2i) q^{17} -111305. i q^{19} +63689.3 q^{21} +(142842. - 142842. i) q^{23} +(-152904. - 152904. i) q^{27} +945318. i q^{29} -674325. q^{31} +(99178.3 - 99178.3i) q^{33} +(1.18332e6 + 1.18332e6i) q^{37} +36977.9i q^{39} +3.81303e6 q^{41} +(3.55470e6 - 3.55470e6i) q^{43} +(3.09808e6 + 3.09808e6i) q^{47} +8.53335e6i q^{49} -948755. q^{51} +(3.90661e6 - 3.90661e6i) q^{53} +(1.32564e6 + 1.32564e6i) q^{57} +2.24160e7i q^{59} -5.70972e6 q^{61} +(1.67841e7 - 1.67841e7i) q^{63} +(1.68179e7 + 1.68179e7i) q^{67} +3.40250e6i q^{69} +3.93208e7 q^{71} +(3.75805e7 - 3.75805e7i) q^{73} +(2.22654e7 + 2.22654e7i) q^{77} +2.25314e7i q^{79} -3.75432e7 q^{81} +(-9.55460e6 + 9.55460e6i) q^{83} +(-1.12587e7 - 1.12587e7i) q^{87} +9.37891e7i q^{89} -8.30148e6 q^{91} +(8.03121e6 - 8.03121e6i) q^{93} +(-1.82973e7 - 1.82973e7i) q^{97} -5.22731e7i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 420 q^{11} - 921168 q^{21} + 3833112 q^{31} + 3587532 q^{41} + 46092564 q^{51} + 31354704 q^{61} - 29589384 q^{71} + 104018868 q^{81} + 433229088 q^{91}+O(q^{100}) $ 12 * q - 420 * q^11 - 921168 * q^21 + 3833112 * q^31 + 3587532 * q^41 + 46092564 * q^51 + 31354704 * q^61 - 29589384 * q^71 + 104018868 * q^81 + 433229088 * q^91

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−11.9100	+	11.9100i	−0.147037	+	0.147037i	−0.776793	−	0.629756i	$-0.783155\pi$
$3$	−11.9100	+	11.9100i	−0.147037	+	0.147037i	0.629756	+	0.776793i	$0.283155\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2673.78	−	2673.78i	−1.11361	−	1.11361i	−0.992659	−	0.120950i	$-0.961406\pi$
$7$	−2673.78	−	2673.78i	−1.11361	−	1.11361i	−0.120950	−	0.992659i	$-0.538594\pi$
$8$		0			0
$9$			6277.30i			0.956760i
$10$		0			0
$11$	−8327.31			−0.568767			−0.284383	−	0.958711i	$-0.591789\pi$
$11$	−8327.31			−0.568767			−0.284383	+	0.958711i	$0.591789\pi$
$12$		0			0
$13$	1552.39	−	1552.39i	0.0543535	−	0.0543535i	−0.679408	−	0.733761i	$-0.737763\pi$
$13$	1552.39	−	1552.39i	0.0543535	−	0.0543535i	0.733761	+	0.679408i	$0.237763\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	39830.2	+	39830.2i	0.476888	+	0.476888i	0.904135	−	0.427247i	$-0.140517\pi$
$17$	39830.2	+	39830.2i	0.476888	+	0.476888i	−0.427247	+	0.904135i	$0.640517\pi$
$18$		0			0
$19$		−	111305.i		−	0.854083i	−0.904232	−	0.427042i	$-0.859556\pi$
$19$		−	111305.i		−	0.854083i	0.904232	−	0.427042i	$-0.140444\pi$
$20$		0			0
$21$	63689.3			0.327484
$22$		0			0
$23$	142842.	−	142842.i	0.510441	−	0.510441i	−0.404221	−	0.914661i	$-0.632457\pi$
$23$	142842.	−	142842.i	0.510441	−	0.510441i	0.914661	+	0.404221i	$0.132457\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−152904.	−	152904.i	−0.287716	−	0.287716i
$28$		0			0
$29$			945318.i			1.33655i	0.743913	+	0.668276i	$0.232968\pi$
$29$			945318.i			1.33655i	−0.743913	+	0.668276i	$0.767032\pi$
$30$		0			0
$31$	−674325.			−0.730167			−0.365084	−	0.930975i	$-0.618960\pi$
$31$	−674325.			−0.730167			−0.365084	+	0.930975i	$0.618960\pi$
$32$		0			0
$33$	99178.3	−	99178.3i	0.0836298	−	0.0836298i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.18332e6	+	1.18332e6i	0.631384	+	0.631384i	0.948415	−	0.317031i	$-0.102686\pi$
$37$	1.18332e6	+	1.18332e6i	0.631384	+	0.631384i	−0.317031	+	0.948415i	$0.602686\pi$
$38$		0			0
$39$			36977.9i			0.0159840i
$40$		0			0
$41$	3.81303e6			1.34938			0.674690	−	0.738101i	$-0.264277\pi$
$41$	3.81303e6			1.34938			0.674690	+	0.738101i	$0.264277\pi$
$42$		0			0
$43$	3.55470e6	−	3.55470e6i	1.03975	−	1.03975i	0.0405753	−	0.999176i	$-0.487081\pi$
$43$	3.55470e6	−	3.55470e6i	1.03975	−	1.03975i	0.999176	−	0.0405753i	$-0.0129191\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.09808e6	+	3.09808e6i	0.634894	+	0.634894i	0.949291	−	0.314397i	$-0.101802\pi$
$47$	3.09808e6	+	3.09808e6i	0.634894	+	0.634894i	−0.314397	+	0.949291i	$0.601802\pi$
$48$		0			0
$49$			8.53335e6i			1.48025i
$50$		0			0
$51$	−948755.			−0.140240
$52$		0			0
$53$	3.90661e6	−	3.90661e6i	0.495104	−	0.495104i	−0.414806	−	0.909910i	$-0.636150\pi$
$53$	3.90661e6	−	3.90661e6i	0.495104	−	0.495104i	0.909910	+	0.414806i	$0.136150\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	1.32564e6	+	1.32564e6i	0.125582	+	0.125582i
$58$		0			0
$59$			2.24160e7i			1.84991i	0.380077	+	0.924955i	$0.375897\pi$
$59$			2.24160e7i			1.84991i	−0.380077	+	0.924955i	$0.624103\pi$
$60$		0			0
$61$	−5.70972e6			−0.412378			−0.206189	−	0.978512i	$-0.566106\pi$
$61$	−5.70972e6			−0.412378			−0.206189	+	0.978512i	$0.566106\pi$
$62$		0			0
$63$	1.67841e7	−	1.67841e7i	1.06546	−	1.06546i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	1.68179e7	+	1.68179e7i	0.834590	+	0.834590i	0.988141	−	0.153551i	$-0.0490709\pi$
$67$	1.68179e7	+	1.68179e7i	0.834590	+	0.834590i	−0.153551	+	0.988141i	$0.549071\pi$
$68$		0			0
$69$			3.40250e6i			0.150107i
$70$		0			0
$71$	3.93208e7			1.54735			0.773675	−	0.633582i	$-0.218416\pi$
$71$	3.93208e7			1.54735			0.773675	+	0.633582i	$0.218416\pi$
$72$		0			0
$73$	3.75805e7	−	3.75805e7i	1.32334	−	1.32334i	0.412281	−	0.911057i	$-0.364732\pi$
$73$	3.75805e7	−	3.75805e7i	1.32334	−	1.32334i	0.911057	−	0.412281i	$-0.135268\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.22654e7	+	2.22654e7i	0.633384	+	0.633384i
$78$		0			0
$79$			2.25314e7i			0.578470i	0.957258	+	0.289235i	$0.0934009\pi$
$79$			2.25314e7i			0.578470i	−0.957258	+	0.289235i	$0.906599\pi$
$80$		0			0
$81$	−3.75432e7			−0.872150
$82$		0			0
$83$	−9.55460e6	+	9.55460e6i	−0.201326	+	0.201326i	−0.800568	−	0.599242i	$-0.795469\pi$
$83$	−9.55460e6	+	9.55460e6i	−0.201326	+	0.201326i	0.599242	+	0.800568i	$0.295469\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−1.12587e7	−	1.12587e7i	−0.196523	−	0.196523i
$88$		0			0
$89$			9.37891e7i			1.49483i	0.664356	+	0.747416i	$0.268706\pi$
$89$			9.37891e7i			1.49483i	−0.664356	+	0.747416i	$0.731294\pi$
$90$		0			0
$91$	−8.30148e6			−0.121057
$92$		0			0
$93$	8.03121e6	−	8.03121e6i	0.107362	−	0.107362i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−1.82973e7	−	1.82973e7i	−0.206681	−	0.206681i	0.596174	−	0.802855i	$-0.296687\pi$
$97$	−1.82973e7	−	1.82973e7i	−0.206681	−	0.206681i	−0.802855	+	0.596174i	$0.796687\pi$
$98$		0			0
$99$		−	5.22731e7i		−	0.544173i
$100$		0			0
$101$	9.10075e7			0.874565			0.437282	−	0.899324i	$-0.355941\pi$
$101$	9.10075e7			0.874565			0.437282	+	0.899324i	$0.355941\pi$
$102$		0			0
$103$	1.07471e7	−	1.07471e7i	0.0954863	−	0.0954863i	−0.657750	−	0.753236i	$-0.728492\pi$
$103$	1.07471e7	−	1.07471e7i	0.0954863	−	0.0954863i	0.753236	+	0.657750i	$0.228492\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.19976e7	+	1.19976e7i	0.0915289	+	0.0915289i	0.751389	−	0.659860i	$-0.229384\pi$
$107$	1.19976e7	+	1.19976e7i	0.0915289	+	0.0915289i	−0.659860	+	0.751389i	$0.729384\pi$
$108$		0			0
$109$		−	1.78253e8i		−	1.26279i	−0.775461	−	0.631395i	$-0.782483\pi$
$109$		−	1.78253e8i		−	1.26279i	0.775461	−	0.631395i	$-0.217517\pi$
$110$		0			0
$111$	−2.81866e7			−0.185674
$112$		0			0
$113$	−1.83187e8	+	1.83187e8i	−1.12352	+	1.12352i	−0.132310	+	0.991208i	$0.542239\pi$
$113$	−1.83187e8	+	1.83187e8i	−1.12352	+	1.12352i	−0.991208	+	0.132310i	$0.957761\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	9.74482e6	+	9.74482e6i	0.0520032	+	0.0520032i
$118$		0			0
$119$		−	2.12994e8i		−	1.06213i
$120$		0			0
$121$	−1.45015e8			−0.676505
$122$		0			0
$123$	−4.54132e7	+	4.54132e7i	−0.198409	+	0.198409i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−2.74492e8	−	2.74492e8i	−1.05515	−	1.05515i	−0.998388	−	0.0567647i	$-0.981922\pi$
$127$	−2.74492e8	−	2.74492e8i	−1.05515	−	1.05515i	−0.0567647	−	0.998388i	$-0.518078\pi$
$128$		0			0
$129$			8.46731e7i			0.305764i
$130$		0			0
$131$	−1.67350e8			−0.568250			−0.284125	−	0.958787i	$-0.591703\pi$
$131$	−1.67350e8			−0.568250			−0.284125	+	0.958787i	$0.591703\pi$
$132$		0			0
$133$	−2.97604e8	+	2.97604e8i	−0.951115	+	0.951115i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2.36681e8	−	2.36681e8i	−0.671863	−	0.671863i	0.286282	−	0.958145i	$-0.407581\pi$
$137$	−2.36681e8	−	2.36681e8i	−0.671863	−	0.671863i	−0.958145	+	0.286282i	$0.907581\pi$
$138$		0			0
$139$		−	3.00902e8i		−	0.806058i	−0.915187	−	0.403029i	$-0.867957\pi$
$139$		−	3.00902e8i		−	0.806058i	0.915187	−	0.403029i	$-0.132043\pi$
$140$		0			0
$141$	−7.37963e7			−0.186706
$142$		0			0
$143$	−1.29272e7	+	1.29272e7i	−0.0309144	+	0.0309144i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−1.01632e8	−	1.01632e8i	−0.217652	−	0.217652i
$148$		0			0
$149$		−	9.18968e8i		−	1.86447i	−0.361855	−	0.932234i	$-0.617857\pi$
$149$		−	9.18968e8i		−	1.86447i	0.361855	−	0.932234i	$-0.382143\pi$
$150$		0			0
$151$	5.36821e8			1.03258			0.516288	−	0.856415i	$-0.327314\pi$
$151$	5.36821e8			1.03258			0.516288	+	0.856415i	$0.327314\pi$
$152$		0			0
$153$	−2.50026e8	+	2.50026e8i	−0.456267	+	0.456267i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	6.75635e8	+	6.75635e8i	1.11202	+	1.11202i	0.992877	+	0.119146i	$0.0380157\pi$
$157$	6.75635e8	+	6.75635e8i	1.11202	+	1.11202i	0.119146	+	0.992877i	$0.461984\pi$
$158$		0			0
$159$			9.30555e7i			0.145597i
$160$		0			0
$161$	−7.63856e8			−1.13686
$162$		0			0
$163$	−3.55120e8	+	3.55120e8i	−0.503066	+	0.503066i	−0.912389	−	0.409323i	$-0.865765\pi$
$163$	−3.55120e8	+	3.55120e8i	−0.503066	+	0.503066i	0.409323	+	0.912389i	$0.365765\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−3.94057e8	−	3.94057e8i	−0.506633	−	0.506633i	0.406859	−	0.913491i	$-0.366624\pi$
$167$	−3.94057e8	−	3.94057e8i	−0.506633	−	0.506633i	−0.913491	+	0.406859i	$0.866624\pi$
$168$		0			0
$169$			8.10911e8i			0.994091i
$170$		0			0
$171$	6.98695e8			0.817153
$172$		0			0
$173$	8.01956e8	−	8.01956e8i	0.895295	−	0.895295i	−0.0997201	−	0.995016i	$-0.531795\pi$
$173$	8.01956e8	−	8.01956e8i	0.895295	−	0.895295i	0.995016	+	0.0997201i	$0.0317947\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−2.66975e8	−	2.66975e8i	−0.272005	−	0.272005i
$178$		0			0
$179$			7.56517e8i			0.736896i	0.929648	+	0.368448i	$0.120111\pi$
$179$			7.56517e8i			0.736896i	−0.929648	+	0.368448i	$0.879889\pi$
$180$		0			0
$181$	−3.34842e8			−0.311980			−0.155990	−	0.987759i	$-0.549857\pi$
$181$	−3.34842e8			−0.311980			−0.155990	+	0.987759i	$0.549857\pi$
$182$		0			0
$183$	6.80028e7	−	6.80028e7i	0.0606348	−	0.0606348i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−3.31678e8	−	3.31678e8i	−0.271238	−	0.271238i
$188$		0			0
$189$			8.17663e8i			0.640807i
$190$		0			0
$191$	6.37860e8			0.479283			0.239642	−	0.970861i	$-0.422970\pi$
$191$	6.37860e8			0.479283			0.239642	+	0.970861i	$0.422970\pi$
$192$		0			0
$193$	3.42784e8	−	3.42784e8i	0.247054	−	0.247054i	−0.572707	−	0.819760i	$-0.694107\pi$
$193$	3.42784e8	−	3.42784e8i	0.247054	−	0.247054i	0.819760	+	0.572707i	$0.194107\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	2.08357e9	+	2.08357e9i	1.38338	+	1.38338i	0.838532	+	0.544852i	$0.183414\pi$
$197$	2.08357e9	+	2.08357e9i	1.38338	+	1.38338i	0.544852	+	0.838532i	$0.316586\pi$
$198$		0			0
$199$			2.08289e8i			0.132817i	0.997793	+	0.0664087i	$0.0211541\pi$
$199$			2.08289e8i			0.132817i	−0.997793	+	0.0664087i	$0.978846\pi$
$200$		0			0
$201$	−4.00603e8			−0.245431
$202$		0			0
$203$	2.52757e9	−	2.52757e9i	1.48840	−	1.48840i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	8.96664e8	+	8.96664e8i	0.488369	+	0.488369i
$208$		0			0
$209$			9.26871e8i			0.485774i
$210$		0			0
$211$	1.10992e9			0.559967			0.279984	−	0.960005i	$-0.409671\pi$
$211$	1.10992e9			0.559967			0.279984	+	0.960005i	$0.409671\pi$
$212$		0			0
$213$	−4.68311e8	+	4.68311e8i	−0.227518	+	0.227518i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	1.80299e9	+	1.80299e9i	0.813121	+	0.813121i
$218$		0			0
$219$			8.95167e8i			0.389159i
$220$		0			0
$221$	1.23664e8			0.0518410
$222$		0			0
$223$	3.19309e9	−	3.19309e9i	1.29120	−	1.29120i	0.357149	−	0.934048i	$-0.383749\pi$
$223$	3.19309e9	−	3.19309e9i	1.29120	−	1.29120i	0.934048	−	0.357149i	$-0.116251\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−3.14431e9	−	3.14431e9i	−1.18419	−	1.18419i	−0.978648	−	0.205544i	$-0.934104\pi$
$227$	−3.14431e9	−	3.14431e9i	−1.18419	−	1.18419i	−0.205544	−	0.978648i	$-0.565896\pi$
$228$		0			0
$229$			3.03285e9i			1.10283i	0.834230	+	0.551416i	$0.185912\pi$
$229$			3.03285e9i			1.10283i	−0.834230	+	0.551416i	$0.814088\pi$
$230$		0			0
$231$	−5.30361e8			−0.186262
$232$		0			0
$233$	−2.36009e9	+	2.36009e9i	−0.800763	+	0.800763i	−0.983215	−	0.182452i	$-0.941597\pi$
$233$	−2.36009e9	+	2.36009e9i	−0.800763	+	0.800763i	0.182452	+	0.983215i	$0.441597\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−2.68350e8	−	2.68350e8i	−0.0850565	−	0.0850565i
$238$		0			0
$239$			1.48671e9i			0.455655i	0.973702	+	0.227827i	$0.0731622\pi$
$239$			1.48671e9i			0.455655i	−0.973702	+	0.227827i	$0.926838\pi$
$240$		0			0
$241$	−2.17060e9			−0.643447			−0.321723	−	0.946834i	$-0.604262\pi$
$241$	−2.17060e9			−0.643447			−0.321723	+	0.946834i	$0.604262\pi$
$242$		0			0
$243$	1.45034e9	−	1.45034e9i	0.415955	−	0.415955i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−1.72789e8	−	1.72789e8i	−0.0464224	−	0.0464224i
$248$		0			0
$249$		−	2.27591e8i		−	0.0592048i
$250$		0			0
$251$	5.99212e9			1.50968			0.754841	−	0.655908i	$-0.227714\pi$
$251$	5.99212e9			1.50968			0.754841	+	0.655908i	$0.227714\pi$
$252$		0			0
$253$	−1.18949e9	+	1.18949e9i	−0.290322	+	0.290322i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	4.93575e9	+	4.93575e9i	1.13141	+	1.13141i	0.989943	+	0.141469i	$0.0451827\pi$
$257$	4.93575e9	+	4.93575e9i	1.13141	+	1.13141i	0.141469	+	0.989943i	$0.454817\pi$
$258$		0			0
$259$		−	6.32784e9i		−	1.40623i
$260$		0			0
$261$	−5.93405e9			−1.27876
$262$		0			0
$263$	−3.36075e9	+	3.36075e9i	−0.702447	+	0.702447i	−0.964935	−	0.262488i	$-0.915457\pi$
$263$	−3.36075e9	+	3.36075e9i	−0.702447	+	0.702447i	0.262488	+	0.964935i	$0.415457\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−1.11703e9	−	1.11703e9i	−0.219796	−	0.219796i
$268$		0			0
$269$		−	2.72431e9i		−	0.520292i	−0.965569	−	0.260146i	$-0.916229\pi$
$269$		−	2.72431e9i		−	0.520292i	0.965569	−	0.260146i	$-0.0837707\pi$
$270$		0			0
$271$	3.22189e9			0.597357			0.298679	−	0.954354i	$-0.403454\pi$
$271$	3.22189e9			0.597357			0.298679	+	0.954354i	$0.403454\pi$
$272$		0			0
$273$	9.88707e7	−	9.88707e7i	0.0177999	−	0.0177999i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−3.52326e9	−	3.52326e9i	−0.598448	−	0.598448i	0.341452	−	0.939899i	$-0.389081\pi$
$277$	−3.52326e9	−	3.52326e9i	−0.598448	−	0.598448i	−0.939899	+	0.341452i	$0.889081\pi$
$278$		0			0
$279$		−	4.23294e9i		−	0.698595i
$280$		0			0
$281$	8.99035e8			0.144195			0.0720976	−	0.997398i	$-0.477031\pi$
$281$	8.99035e8			0.144195			0.0720976	+	0.997398i	$0.477031\pi$
$282$		0			0
$283$	−5.06850e9	+	5.06850e9i	−0.790193	+	0.790193i	−0.981525	−	0.191332i	$-0.938719\pi$
$283$	−5.06850e9	+	5.06850e9i	−0.790193	+	0.790193i	0.191332	+	0.981525i	$0.438719\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−1.01952e10	−	1.01952e10i	−1.50268	−	1.50268i
$288$		0			0
$289$		−	3.80287e9i		−	0.545156i
$290$		0			0
$291$	4.35842e8			0.0607795
$292$		0			0
$293$	−3.80587e9	+	3.80587e9i	−0.516397	+	0.516397i	−0.916479	−	0.400082i	$-0.868981\pi$
$293$	−3.80587e9	+	3.80587e9i	−0.516397	+	0.516397i	0.400082	+	0.916479i	$0.368981\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	1.27328e9	+	1.27328e9i	0.163643	+	0.163643i
$298$		0			0
$299$		−	4.43494e8i		−	0.0554884i
$300$		0			0
$301$	−1.90090e10			−2.31575
$302$		0			0
$303$	−1.08390e9	+	1.08390e9i	−0.128593	+	0.128593i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−9.82709e8	−	9.82709e8i	−0.110630	−	0.110630i	0.649625	−	0.760255i	$-0.274926\pi$
$307$	−9.82709e8	−	9.82709e8i	−0.110630	−	0.110630i	−0.760255	+	0.649625i	$0.774926\pi$
$308$		0			0
$309$			2.55995e8i			0.0280800i
$310$		0			0
$311$	7.76262e9			0.829787			0.414894	−	0.909870i	$-0.363819\pi$
$311$	7.76262e9			0.829787			0.414894	+	0.909870i	$0.363819\pi$
$312$		0			0
$313$	−6.87570e9	+	6.87570e9i	−0.716374	+	0.716374i	−0.967861	−	0.251487i	$-0.919080\pi$
$313$	−6.87570e9	+	6.87570e9i	−0.716374	+	0.716374i	0.251487	+	0.967861i	$0.419080\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−8.40609e8	−	8.40609e8i	−0.0832448	−	0.0832448i	0.664258	−	0.747503i	$-0.268747\pi$
$317$	−8.40609e8	−	8.40609e8i	−0.0832448	−	0.0832448i	−0.747503	+	0.664258i	$0.768747\pi$
$318$		0			0
$319$		−	7.87196e9i		−	0.760186i
$320$		0			0
$321$	−2.85782e8			−0.0269163
$322$		0			0
$323$	4.43329e9	−	4.43329e9i	0.407302	−	0.407302i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	2.12300e9	+	2.12300e9i	0.185677	+	0.185677i
$328$		0			0
$329$		−	1.65671e10i		−	1.41405i
$330$		0			0
$331$	5.50121e9			0.458296			0.229148	−	0.973392i	$-0.426406\pi$
$331$	5.50121e9			0.458296			0.229148	+	0.973392i	$0.426406\pi$
$332$		0			0
$333$	−7.42803e9	+	7.42803e9i	−0.604084	+	0.604084i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	9.38218e9	+	9.38218e9i	0.727418	+	0.727418i	0.970105	−	0.242687i	$-0.0780286\pi$
$337$	9.38218e9	+	9.38218e9i	0.727418	+	0.727418i	−0.242687	+	0.970105i	$0.578029\pi$
$338$		0			0
$339$		−	4.36351e9i		−	0.330398i
$340$		0			0
$341$	5.61531e9			0.415295
$342$		0			0
$343$	7.40247e9	−	7.40247e9i	0.534811	−	0.534811i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−1.32838e10	−	1.32838e10i	−0.916232	−	0.916232i	0.0805208	−	0.996753i	$-0.474342\pi$
$347$	−1.32838e10	−	1.32838e10i	−0.916232	−	0.916232i	−0.996753	+	0.0805208i	$0.974342\pi$
$348$		0			0
$349$			2.03901e10i			1.37441i	0.726461	+	0.687207i	$0.241164\pi$
$349$			2.03901e10i			1.37441i	−0.726461	+	0.687207i	$0.758836\pi$
$350$		0			0
$351$	−4.74734e8			−0.0312768
$352$		0			0
$353$	6.47303e9	−	6.47303e9i	0.416878	−	0.416878i	−0.467249	−	0.884126i	$-0.654755\pi$
$353$	6.47303e9	−	6.47303e9i	0.416878	−	0.416878i	0.884126	+	0.467249i	$0.154755\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	2.53676e9	+	2.53676e9i	0.156173	+	0.156173i
$358$		0			0
$359$			1.76783e10i			1.06430i	0.846651	+	0.532148i	$0.178615\pi$
$359$			1.76783e10i			1.06430i	−0.846651	+	0.532148i	$0.821385\pi$
$360$		0			0
$361$	4.59477e9			0.270542
$362$		0			0
$363$	1.72713e9	−	1.72713e9i	0.0994713	−	0.0994713i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	4.59142e9	+	4.59142e9i	0.253095	+	0.253095i	0.822238	−	0.569143i	$-0.192725\pi$
$367$	4.59142e9	+	4.59142e9i	0.253095	+	0.253095i	−0.569143	+	0.822238i	$0.692725\pi$
$368$		0			0
$369$			2.39355e10i			1.29103i
$370$		0			0
$371$	−2.08908e10			−1.10271
$372$		0			0
$373$	−3.21331e9	+	3.21331e9i	−0.166004	+	0.166004i	−0.785220	−	0.619217i	$-0.787450\pi$
$373$	−3.21331e9	+	3.21331e9i	−0.166004	+	0.166004i	0.619217	+	0.785220i	$0.287450\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	1.46750e9	+	1.46750e9i	0.0726463	+	0.0726463i
$378$		0			0
$379$			1.41224e10i			0.684466i	0.939615	+	0.342233i	$0.111183\pi$
$379$			1.41224e10i			0.684466i	−0.939615	+	0.342233i	$0.888817\pi$
$380$		0			0
$381$	6.53841e9			0.310293
$382$		0			0
$383$	2.66112e10	−	2.66112e10i	1.23671	−	1.23671i	0.275376	−	0.961337i	$-0.411198\pi$
$383$	2.66112e10	−	2.66112e10i	1.23671	−	1.23671i	0.961337	−	0.275376i	$-0.0888022\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	2.23140e10	+	2.23140e10i	0.994793	+	0.994793i
$388$		0			0
$389$		−	8.40575e9i		−	0.367095i	−0.983011	−	0.183547i	$-0.941242\pi$
$389$		−	8.40575e9i		−	0.367095i	0.983011	−	0.183547i	$-0.0587580\pi$
$390$		0			0
$391$	1.13789e10			0.486846
$392$		0			0
$393$	1.99313e9	−	1.99313e9i	0.0835538	−	0.0835538i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	1.44267e10	+	1.44267e10i	0.580773	+	0.580773i	0.935116	−	0.354343i	$-0.115295\pi$
$397$	1.44267e10	+	1.44267e10i	0.580773	+	0.580773i	−0.354343	+	0.935116i	$0.615295\pi$
$398$		0			0
$399$		−	7.08894e9i		−	0.279698i
$400$		0			0
$401$	2.40043e10			0.928349			0.464175	−	0.885744i	$-0.346351\pi$
$401$	2.40043e10			0.928349			0.464175	+	0.885744i	$0.346351\pi$
$402$		0			0
$403$	−1.04681e9	+	1.04681e9i	−0.0396871	+	0.0396871i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−9.85384e9	−	9.85384e9i	−0.359110	−	0.359110i
$408$		0			0
$409$			1.72270e10i			0.615625i	0.951447	+	0.307813i	$0.0995970\pi$
$409$			1.72270e10i			0.615625i	−0.951447	+	0.307813i	$0.900403\pi$
$410$		0			0
$411$	5.63774e9			0.197578
$412$		0			0
$413$	5.99354e10	−	5.99354e10i	2.06008	−	2.06008i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	3.58374e9	+	3.58374e9i	0.118520	+	0.118520i
$418$		0			0
$419$			1.11113e10i			0.360501i	0.983621	+	0.180251i	$0.0576909\pi$
$419$			1.11113e10i			0.360501i	−0.983621	+	0.180251i	$0.942309\pi$
$420$		0			0
$421$	−1.30583e10			−0.415679			−0.207840	−	0.978163i	$-0.566643\pi$
$421$	−1.30583e10			−0.415679			−0.207840	+	0.978163i	$0.566643\pi$
$422$		0			0
$423$	−1.94476e10	+	1.94476e10i	−0.607441	+	0.607441i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	1.52665e10	+	1.52665e10i	0.459228	+	0.459228i
$428$		0			0
$429$		−	3.07927e8i		−	0.00909114i
$430$		0			0
$431$	1.06253e10			0.307915			0.153958	−	0.988077i	$-0.450798\pi$
$431$	1.06253e10			0.307915			0.153958	+	0.988077i	$0.450798\pi$
$432$		0			0
$433$	3.71745e9	−	3.71745e9i	0.105753	−	0.105753i	−0.652250	−	0.758004i	$-0.726175\pi$
$433$	3.71745e9	−	3.71745e9i	0.105753	−	0.105753i	0.758004	+	0.652250i	$0.226175\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.58990e10	−	1.58990e10i	−0.435959	−	0.435959i
$438$		0			0
$439$			4.79759e10i			1.29171i	0.763460	+	0.645856i	$0.223499\pi$
$439$			4.79759e10i			1.29171i	−0.763460	+	0.645856i	$0.776501\pi$
$440$		0			0
$441$	−5.35664e10			−1.41624
$442$		0			0
$443$	−2.87652e10	+	2.87652e10i	−0.746884	+	0.746884i	−0.973893	−	0.227009i	$-0.927105\pi$
$443$	−2.87652e10	+	2.87652e10i	−0.746884	+	0.746884i	0.227009	+	0.973893i	$0.427105\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	1.09449e10	+	1.09449e10i	0.274146	+	0.274146i
$448$		0			0
$449$		−	5.35257e8i		−	0.0131697i	−0.999978	−	0.00658487i	$-0.997904\pi$
$449$		−	5.35257e8i		−	0.0131697i	0.999978	−	0.00658487i	$-0.00209604\pi$
$450$		0			0
$451$	−3.17523e10			−0.767483
$452$		0			0
$453$	−6.39354e9	+	6.39354e9i	−0.151827	+	0.151827i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−3.94518e10	−	3.94518e10i	−0.904487	−	0.904487i	0.0913331	−	0.995820i	$-0.470887\pi$
$457$	−3.94518e10	−	3.94518e10i	−0.904487	−	0.904487i	−0.995820	+	0.0913331i	$0.970887\pi$
$458$		0			0
$459$		−	1.21804e10i		−	0.274417i
$460$		0			0
$461$	7.52433e10			1.66596			0.832979	−	0.553304i	$-0.186633\pi$
$461$	7.52433e10			1.66596			0.832979	+	0.553304i	$0.186633\pi$
$462$		0			0
$463$	−2.51732e9	+	2.51732e9i	−0.0547790	+	0.0547790i	−0.733966	−	0.679187i	$-0.762333\pi$
$463$	−2.51732e9	+	2.51732e9i	−0.0547790	+	0.0547790i	0.679187	+	0.733966i	$0.262333\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−2.24180e10	−	2.24180e10i	−0.471336	−	0.471336i	0.431011	−	0.902347i	$-0.358157\pi$
$467$	−2.24180e10	−	2.24180e10i	−0.471336	−	0.471336i	−0.902347	+	0.431011i	$0.858157\pi$
$468$		0			0
$469$		−	8.99347e10i		−	1.85881i
$470$		0			0
$471$	−1.60936e10			−0.327017
$472$		0			0
$473$	−2.96011e10	+	2.96011e10i	−0.591376	+	0.591376i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	2.45230e10	+	2.45230e10i	0.473696	+	0.473696i
$478$		0			0
$479$		−	3.13058e10i		−	0.594679i	−0.954772	−	0.297340i	$-0.903901\pi$
$479$		−	3.13058e10i		−	0.594679i	0.954772	−	0.297340i	$-0.0960994\pi$
$480$		0			0
$481$	3.67394e9			0.0686359
$482$		0			0
$483$	9.09753e9	−	9.09753e9i	0.167161	−	0.167161i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	6.95947e10	+	6.95947e10i	1.23726	+	1.23726i	0.961117	+	0.276142i	$0.0890559\pi$
$487$	6.95947e10	+	6.95947e10i	1.23726	+	1.23726i	0.276142	+	0.961117i	$0.410944\pi$
$488$		0			0
$489$		−	8.45897e9i		−	0.147939i
$490$		0			0
$491$	6.69710e10			1.15229			0.576143	−	0.817349i	$-0.304557\pi$
$491$	6.69710e10			1.15229			0.576143	+	0.817349i	$0.304557\pi$
$492$		0			0
$493$	−3.76522e10	+	3.76522e10i	−0.637386	+	0.637386i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.05135e11	−	1.05135e11i	−1.72314	−	1.72314i
$498$		0			0
$499$		−	7.63925e10i		−	1.23211i	−0.787704	−	0.616054i	$-0.788730\pi$
$499$		−	7.63925e10i		−	1.23211i	0.787704	−	0.616054i	$-0.211270\pi$
$500$		0			0
$501$	9.38644e9			0.148988
$502$		0			0
$503$	−3.82330e10	+	3.82330e10i	−0.597264	+	0.597264i	−0.939584	−	0.342319i	$-0.888787\pi$
$503$	−3.82330e10	+	3.82330e10i	−0.597264	+	0.597264i	0.342319	+	0.939584i	$0.388787\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−9.65795e9	−	9.65795e9i	−0.146168	−	0.146168i
$508$		0			0
$509$		−	1.48548e10i		−	0.221307i	−0.993859	−	0.110653i	$-0.964706\pi$
$509$		−	1.48548e10i		−	0.221307i	0.993859	−	0.110653i	$-0.0352944\pi$
$510$		0			0
$511$	−2.00963e11			−2.94736
$512$		0			0
$513$	−1.70190e10	+	1.70190e10i	−0.245734	+	0.245734i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−2.57987e10	−	2.57987e10i	−0.361106	−	0.361106i
$518$		0			0
$519$			1.91026e10i			0.263283i
$520$		0			0
$521$	1.01864e11			1.38251			0.691255	−	0.722611i	$-0.257058\pi$
$521$	1.01864e11			1.38251			0.691255	+	0.722611i	$0.257058\pi$
$522$		0			0
$523$	−8.63327e10	+	8.63327e10i	−1.15390	+	1.15390i	−0.168138	+	0.985763i	$0.553775\pi$
$523$	−8.63327e10	+	8.63327e10i	−1.15390	+	1.15390i	−0.985763	+	0.168138i	$0.946225\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.68585e10	−	2.68585e10i	−0.348208	−	0.348208i
$528$		0			0
$529$			3.75032e10i			0.478901i
$530$		0			0
$531$	−1.40712e11			−1.76992
$532$		0			0
$533$	5.91930e9	−	5.91930e9i	0.0733435	−	0.0733435i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−9.01012e9	−	9.01012e9i	−0.108351	−	0.108351i
$538$		0			0
$539$		−	7.10598e10i		−	0.841917i
$540$		0			0
$541$	3.24389e10			0.378684			0.189342	−	0.981911i	$-0.439365\pi$
$541$	3.24389e10			0.378684			0.189342	+	0.981911i	$0.439365\pi$
$542$		0			0
$543$	3.98797e9	−	3.98797e9i	0.0458726	−	0.0458726i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	8.37039e9	+	8.37039e9i	0.0934967	+	0.0934967i	0.752308	−	0.658811i	$-0.228940\pi$
$547$	8.37039e9	+	8.37039e9i	0.0934967	+	0.0934967i	−0.658811	+	0.752308i	$0.728940\pi$
$548$		0			0
$549$		−	3.58416e10i		−	0.394547i
$550$		0			0
$551$	1.05219e11			1.14153
$552$		0			0
$553$	6.02440e10	−	6.02440e10i	0.644189	−	0.644189i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−7.16497e10	−	7.16497e10i	−0.744378	−	0.744378i	0.229039	−	0.973417i	$-0.426442\pi$
$557$	−7.16497e10	−	7.16497e10i	−0.744378	−	0.744378i	−0.973417	+	0.229039i	$0.926442\pi$
$558$		0			0
$559$		−	1.10366e10i		−	0.113028i
$560$		0			0
$561$	7.90058e9			0.0797641
$562$		0			0
$563$	4.16039e10	−	4.16039e10i	0.414096	−	0.414096i	−0.469067	−	0.883163i	$-0.655410\pi$
$563$	4.16039e10	−	4.16039e10i	0.414096	−	0.414096i	0.883163	+	0.469067i	$0.155410\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	1.00382e11	+	1.00382e11i	0.971234	+	0.971234i
$568$		0			0
$569$		−	3.36524e10i		−	0.321046i	−0.987032	−	0.160523i	$-0.948682\pi$
$569$		−	3.36524e10i		−	0.321046i	0.987032	−	0.160523i	$-0.0513180\pi$
$570$		0			0
$571$	7.08708e9			0.0666688			0.0333344	−	0.999444i	$-0.489387\pi$
$571$	7.08708e9			0.0666688			0.0333344	+	0.999444i	$0.489387\pi$
$572$		0			0
$573$	−7.59692e9	+	7.59692e9i	−0.0704724	+	0.0704724i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	8.43390e10	+	8.43390e10i	0.760896	+	0.760896i	0.976484	−	0.215589i	$-0.0691670\pi$
$577$	8.43390e10	+	8.43390e10i	0.760896	+	0.760896i	−0.215589	+	0.976484i	$0.569167\pi$
$578$		0			0
$579$			8.16512e9i			0.0726521i
$580$		0			0
$581$	5.10937e10			0.448397
$582$		0			0
$583$	−3.25316e10	+	3.25316e10i	−0.281599	+	0.281599i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	5.29404e9	+	5.29404e9i	0.0445897	+	0.0445897i	0.729050	−	0.684460i	$-0.239962\pi$
$587$	5.29404e9	+	5.29404e9i	0.0445897	+	0.0445897i	−0.684460	+	0.729050i	$0.739962\pi$
$588$		0			0
$589$			7.50557e10i			0.623623i
$590$		0			0
$591$	−4.96306e10			−0.406818
$592$		0			0
$593$	1.32179e11	−	1.32179e11i	1.06891	−	1.06891i	0.0714696	−	0.997443i	$-0.477231\pi$
$593$	1.32179e11	−	1.32179e11i	1.06891	−	1.06891i	0.997443	−	0.0714696i	$-0.0227689\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−2.48073e9	−	2.48073e9i	−0.0195291	−	0.0195291i
$598$		0			0
$599$			1.23084e11i			0.956078i	0.878339	+	0.478039i	$0.158652\pi$
$599$			1.23084e11i			0.956078i	−0.878339	+	0.478039i	$0.841348\pi$
$600$		0			0
$601$	−4.88138e10			−0.374149			−0.187075	−	0.982346i	$-0.559901\pi$
$601$	−4.88138e10			−0.374149			−0.187075	+	0.982346i	$0.559901\pi$
$602$		0			0
$603$	−1.05571e11	+	1.05571e11i	−0.798503	+	0.798503i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	9.04567e10	+	9.04567e10i	0.666325	+	0.666325i	0.956863	−	0.290538i	$-0.0938344\pi$
$607$	9.04567e10	+	9.04567e10i	0.666325	+	0.666325i	−0.290538	+	0.956863i	$0.593834\pi$
$608$		0			0
$609$			6.02067e10i			0.437699i
$610$		0			0
$611$	9.61886e9			0.0690174
$612$		0			0
$613$	4.45608e10	−	4.45608e10i	0.315581	−	0.315581i	−0.531486	−	0.847067i	$-0.678366\pi$
$613$	4.45608e10	−	4.45608e10i	0.315581	−	0.315581i	0.847067	+	0.531486i	$0.178366\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−1.00326e11	−	1.00326e11i	−0.692264	−	0.692264i	0.270466	−	0.962730i	$-0.412822\pi$
$617$	−1.00326e11	−	1.00326e11i	−0.692264	−	0.692264i	−0.962730	+	0.270466i	$0.912822\pi$
$618$		0			0
$619$			2.60850e11i			1.77676i	0.459110	+	0.888380i	$0.348169\pi$
$619$			2.60850e11i			1.77676i	−0.459110	+	0.888380i	$0.651831\pi$
$620$		0			0
$621$	−4.36824e10			−0.293724
$622$		0			0
$623$	2.50771e11	−	2.50771e11i	1.66466	−	1.66466i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−1.10390e10	−	1.10390e10i	−0.0714268	−	0.0714268i
$628$		0			0
$629$			9.42634e10i			0.602199i
$630$		0			0
$631$	1.66950e11			1.05310			0.526548	−	0.850145i	$-0.323486\pi$
$631$	1.66950e11			1.05310			0.526548	+	0.850145i	$0.323486\pi$
$632$		0			0
$633$	−1.32192e10	+	1.32192e10i	−0.0823359	+	0.0823359i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	1.32471e10	+	1.32471e10i	0.0804567	+	0.0804567i
$638$		0			0
$639$			2.46828e11i			1.48044i
$640$		0			0
$641$	1.22165e11			0.723626			0.361813	−	0.932251i	$-0.382158\pi$
$641$	1.22165e11			0.723626			0.361813	+	0.932251i	$0.382158\pi$
$642$		0			0
$643$	−3.34802e10	+	3.34802e10i	−0.195859	+	0.195859i	−0.798222	−	0.602363i	$-0.794226\pi$
$643$	−3.34802e10	+	3.34802e10i	−0.195859	+	0.195859i	0.602363	+	0.798222i	$0.294226\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	5.56116e10	+	5.56116e10i	0.317357	+	0.317357i	0.847751	−	0.530394i	$-0.177956\pi$
$647$	5.56116e10	+	5.56116e10i	0.317357	+	0.317357i	−0.530394	+	0.847751i	$0.677956\pi$
$648$		0			0
$649$		−	1.86665e11i		−	1.05217i
$650$		0			0
$651$	−4.29473e10			−0.239118
$652$		0			0
$653$	1.94708e11	−	1.94708e11i	1.07086	−	1.07086i	0.0735653	−	0.997290i	$-0.476562\pi$
$653$	1.94708e11	−	1.94708e11i	1.07086	−	1.07086i	0.997290	−	0.0735653i	$-0.0234377\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	2.35904e11	+	2.35904e11i	1.26612	+	1.26612i
$658$		0			0
$659$		−	2.86480e11i		−	1.51898i	−0.650519	−	0.759490i	$-0.725449\pi$
$659$		−	2.86480e11i		−	1.51898i	0.650519	−	0.759490i	$-0.274551\pi$
$660$		0			0
$661$	−2.50082e10			−0.131001			−0.0655007	−	0.997853i	$-0.520864\pi$
$661$	−2.50082e10			−0.131001			−0.0655007	+	0.997853i	$0.520864\pi$
$662$		0			0
$663$	−1.47284e9	+	1.47284e9i	−0.00762255	+	0.00762255i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	1.35031e11	+	1.35031e11i	0.682231	+	0.682231i
$668$		0			0
$669$			7.60595e10i			0.379707i
$670$		0			0
$671$	4.75466e10			0.234547
$672$		0			0
$673$	7.00653e9	−	7.00653e9i	0.0341541	−	0.0341541i	−0.689823	−	0.723978i	$-0.742312\pi$
$673$	7.00653e9	−	7.00653e9i	0.0341541	−	0.0341541i	0.723978	+	0.689823i	$0.242312\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−1.85016e11	−	1.85016e11i	−0.880754	−	0.880754i	0.112857	−	0.993611i	$-0.464000\pi$
$677$	−1.85016e11	−	1.85016e11i	−0.880754	−	0.880754i	−0.993611	+	0.112857i	$0.964000\pi$
$678$		0			0
$679$			9.78457e10i			0.460323i
$680$		0			0
$681$	7.48975e10			0.348240
$682$		0			0
$683$	−1.96203e10	+	1.96203e10i	−0.0901617	+	0.0901617i	−0.750749	−	0.660587i	$-0.770307\pi$
$683$	−1.96203e10	+	1.96203e10i	−0.0901617	+	0.0901617i	0.660587	+	0.750749i	$0.270307\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−3.61213e10	−	3.61213e10i	−0.162157	−	0.162157i
$688$		0			0
$689$		−	1.21292e10i		−	0.0538213i
$690$		0			0
$691$	−2.52605e11			−1.10797			−0.553987	−	0.832525i	$-0.686894\pi$
$691$	−2.52605e11			−1.10797			−0.553987	+	0.832525i	$0.686894\pi$
$692$		0			0
$693$	−1.39766e11	+	1.39766e11i	−0.605996	+	0.605996i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	1.51874e11	+	1.51874e11i	0.643504	+	0.643504i
$698$		0			0
$699$		−	5.62173e10i		−	0.235484i
$700$		0			0
$701$	−2.19968e10			−0.0910934			−0.0455467	−	0.998962i	$-0.514503\pi$
$701$	−2.19968e10			−0.0910934			−0.0455467	+	0.998962i	$0.514503\pi$
$702$		0			0
$703$	1.31709e11	−	1.31709e11i	0.539255	−	0.539255i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−2.43334e11	−	2.43334e11i	−0.973923	−	0.973923i
$708$		0			0
$709$			3.40622e11i			1.34799i	0.738734	+	0.673997i	$0.235424\pi$
$709$			3.40622e11i			1.34799i	−0.738734	+	0.673997i	$0.764576\pi$
$710$		0			0
$711$	−1.41437e11			−0.553457
$712$		0			0
$713$	−9.63220e10	+	9.63220e10i	−0.372707	+	0.372707i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−1.77068e10	−	1.77068e10i	−0.0669981	−	0.0669981i
$718$		0			0
$719$		−	1.45561e11i		−	0.544666i	−0.962203	−	0.272333i	$-0.912205\pi$
$719$		−	1.45561e11i		−	0.544666i	0.962203	−	0.272333i	$-0.0877952\pi$
$720$		0			0
$721$	−5.74705e10			−0.212669
$722$		0			0
$723$	2.58519e10	−	2.58519e10i	0.0946105	−	0.0946105i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−3.13672e11	−	3.13672e11i	−1.12289	−	1.12289i	−0.991304	−	0.131590i	$-0.957992\pi$
$727$	−3.13672e11	−	3.13672e11i	−1.12289	−	1.12289i	−0.131590	−	0.991304i	$-0.542008\pi$
$728$		0			0
$729$		−	2.11774e11i		−	0.749829i
$730$		0			0
$731$	2.83169e11			0.991690
$732$		0			0
$733$	−3.49553e11	+	3.49553e11i	−1.21087	+	1.21087i	−0.240130	+	0.970741i	$0.577190\pi$
$733$	−3.49553e11	+	3.49553e11i	−1.21087	+	1.21087i	−0.970741	+	0.240130i	$0.922810\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.40048e11	−	1.40048e11i	−0.474687	−	0.474687i
$738$		0			0
$739$		−	4.52371e11i		−	1.51676i	−0.651813	−	0.758380i	$-0.725991\pi$
$739$		−	4.52371e11i		−	1.51676i	0.651813	−	0.758380i	$-0.274009\pi$
$740$		0			0
$741$	4.11583e9			0.0136516
$742$		0			0
$743$	3.80702e10	−	3.80702e10i	0.124920	−	0.124920i	−0.641883	−	0.766803i	$-0.721847\pi$
$743$	3.80702e10	−	3.80702e10i	0.124920	−	0.124920i	0.766803	+	0.641883i	$0.221847\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−5.99771e10	−	5.99771e10i	−0.192621	−	0.192621i
$748$		0			0
$749$		−	6.41576e10i		−	0.203855i
$750$		0			0
$751$	−6.32423e10			−0.198815			−0.0994073	−	0.995047i	$-0.531695\pi$
$751$	−6.32423e10			−0.198815			−0.0994073	+	0.995047i	$0.531695\pi$
$752$		0			0
$753$	−7.13661e10	+	7.13661e10i	−0.221979	+	0.221979i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	3.90975e11	+	3.90975e11i	1.19060	+	1.19060i	0.976900	+	0.213699i	$0.0685510\pi$
$757$	3.90975e11	+	3.90975e11i	1.19060	+	1.19060i	0.213699	+	0.976900i	$0.431449\pi$
$758$		0			0
$759$		−	2.83337e10i		−	0.0853761i
$760$		0			0
$761$	−5.65194e10			−0.168523			−0.0842615	−	0.996444i	$-0.526853\pi$
$761$	−5.65194e10			−0.168523			−0.0842615	+	0.996444i	$0.526853\pi$
$762$		0			0
$763$	−4.76609e11	+	4.76609e11i	−1.40625	+	1.40625i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	3.47984e10	+	3.47984e10i	0.100549	+	0.100549i
$768$		0			0
$769$		−	4.65007e11i		−	1.32970i	−0.746976	−	0.664851i	$-0.768495\pi$
$769$		−	4.65007e11i		−	1.32970i	0.746976	−	0.664851i	$-0.231505\pi$
$770$		0			0
$771$	−1.17570e11			−0.332719
$772$		0			0
$773$	−1.29334e11	+	1.29334e11i	−0.362238	+	0.362238i	−0.864636	−	0.502398i	$-0.832451\pi$
$773$	−1.29334e11	+	1.29334e11i	−0.362238	+	0.362238i	0.502398	+	0.864636i	$0.332451\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	7.53646e10	+	7.53646e10i	0.206768	+	0.206768i
$778$		0			0
$779$		−	4.24409e11i		−	1.15248i
$780$		0			0
$781$	−3.27436e11			−0.880081
$782$		0			0
$783$	1.44543e11	−	1.44543e11i	0.384548	−	0.384548i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−2.80027e11	−	2.80027e11i	−0.729964	−	0.729964i	0.240648	−	0.970612i	$-0.422640\pi$
$787$	−2.80027e11	−	2.80027e11i	−0.729964	−	0.729964i	−0.970612	+	0.240648i	$0.922640\pi$
$788$		0			0
$789$		−	8.00531e10i		−	0.206571i
$790$		0			0
$791$	9.79600e11			2.50232
$792$		0			0
$793$	−8.86371e9	+	8.86371e9i	−0.0224142	+	0.0224142i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−1.37265e11	−	1.37265e11i	−0.340194	−	0.340194i	0.516246	−	0.856440i	$-0.327329\pi$
$797$	−1.37265e11	−	1.37265e11i	−0.340194	−	0.340194i	−0.856440	+	0.516246i	$0.827329\pi$
$798$		0			0
$799$			2.46794e11i			0.605547i
$800$		0			0
$801$	−5.88743e11			−1.43020
$802$		0			0
$803$	−3.12944e11	+	3.12944e11i	−0.752670	+	0.752670i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	3.24465e10	+	3.24465e10i	0.0765022	+	0.0765022i
$808$		0			0
$809$			4.88941e11i			1.14147i	0.821136	+	0.570733i	$0.193341\pi$
$809$			4.88941e11i			1.14147i	−0.821136	+	0.570733i	$0.806659\pi$
$810$		0			0
$811$	4.73407e10			0.109434			0.0547169	−	0.998502i	$-0.482574\pi$
$811$	4.73407e10			0.109434			0.0547169	+	0.998502i	$0.482574\pi$
$812$		0			0
$813$	−3.83728e10	+	3.83728e10i	−0.0878337	+	0.0878337i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−3.95656e11	−	3.95656e11i	−0.888034	−	0.888034i
$818$		0			0
$819$		−	5.21109e10i		−	0.115823i
$820$		0			0
$821$	−3.47897e11			−0.765734			−0.382867	−	0.923803i	$-0.625063\pi$
$821$	−3.47897e11			−0.765734			−0.382867	+	0.923803i	$0.625063\pi$
$822$		0			0
$823$	4.32776e11	−	4.32776e11i	0.943329	−	0.943329i	−0.0551488	−	0.998478i	$-0.517563\pi$
$823$	4.32776e11	−	4.32776e11i	0.943329	−	0.943329i	0.998478	+	0.0551488i	$0.0175633\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−4.47219e11	−	4.47219e11i	−0.956090	−	0.956090i	0.0429859	−	0.999076i	$-0.486313\pi$
$827$	−4.47219e11	−	4.47219e11i	−0.956090	−	0.956090i	−0.999076	+	0.0429859i	$0.986313\pi$
$828$		0			0
$829$		−	5.23265e11i		−	1.10791i	−0.832547	−	0.553954i	$-0.813118\pi$
$829$		−	5.23265e11i		−	1.10791i	0.832547	−	0.553954i	$-0.186882\pi$
$830$		0			0
$831$	8.39242e10			0.175988
$832$		0			0
$833$	−3.39885e11	+	3.39885e11i	−0.705913	+	0.705913i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	1.03107e11	+	1.03107e11i	0.210081	+	0.210081i
$838$		0			0
$839$			6.60921e11i			1.33383i	0.745132	+	0.666917i	$0.232386\pi$
$839$			6.60921e11i			1.33383i	−0.745132	+	0.666917i	$0.767614\pi$
$840$		0			0
$841$	−3.93380e11			−0.786373
$842$		0			0
$843$	−1.07075e10	+	1.07075e10i	−0.0212021	+	0.0212021i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	3.87737e11	+	3.87737e11i	0.753362	+	0.753362i
$848$		0			0
$849$		−	1.20732e11i		−	0.232375i
$850$		0			0
$851$	3.38055e11			0.644569
$852$		0			0
$853$	2.31333e11	−	2.31333e11i	0.436959	−	0.436959i	−0.454028	−	0.890987i	$-0.650013\pi$
$853$	2.31333e11	−	2.31333e11i	0.436959	−	0.436959i	0.890987	+	0.454028i	$0.150013\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	5.09154e11	+	5.09154e11i	0.943900	+	0.943900i	0.998508	−	0.0546083i	$-0.0173910\pi$
$857$	5.09154e11	+	5.09154e11i	0.943900	+	0.943900i	−0.0546083	+	0.998508i	$0.517391\pi$
$858$		0			0
$859$		−	7.88585e10i		−	0.144836i	−0.997374	−	0.0724179i	$-0.976928\pi$
$859$		−	7.88585e10i		−	0.144836i	0.997374	−	0.0724179i	$-0.0230715\pi$
$860$		0			0
$861$	2.42849e11			0.441900
$862$		0			0
$863$	3.41621e11	−	3.41621e11i	0.615887	−	0.615887i	−0.328587	−	0.944474i	$-0.606572\pi$
$863$	3.41621e11	−	3.41621e11i	0.615887	−	0.615887i	0.944474	+	0.328587i	$0.106572\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	4.52922e10	+	4.52922e10i	0.0801581	+	0.0801581i
$868$		0			0
$869$		−	1.87626e11i		−	0.329014i
$870$		0			0
$871$	5.22159e10			0.0907257
$872$		0			0
$873$	1.14858e11	−	1.14858e11i	0.197744	−	0.197744i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	6.22499e11	+	6.22499e11i	1.05230	+	1.05230i	0.998555	+	0.0537474i	$0.0171166\pi$
$877$	6.22499e11	+	6.22499e11i	1.05230	+	1.05230i	0.0537474	+	0.998555i	$0.482883\pi$
$878$		0			0
$879$		−	9.06558e10i		−	0.151859i
$880$		0			0
$881$	−8.38509e9			−0.0139189			−0.00695944	−	0.999976i	$-0.502215\pi$
$881$	−8.38509e9			−0.0139189			−0.00695944	+	0.999976i	$0.502215\pi$
$882$		0			0
$883$	3.87671e11	−	3.87671e11i	0.637705	−	0.637705i	−0.312284	−	0.949989i	$-0.601094\pi$
$883$	3.87671e11	−	3.87671e11i	0.637705	−	0.637705i	0.949989	+	0.312284i	$0.101094\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	2.88560e11	+	2.88560e11i	0.466167	+	0.466167i	0.900670	−	0.434503i	$-0.143076\pi$
$887$	2.88560e11	+	2.88560e11i	0.466167	+	0.466167i	−0.434503	+	0.900670i	$0.643076\pi$
$888$		0			0
$889$			1.46786e12i			2.35005i
$890$		0			0
$891$	3.12634e11			0.496050
$892$		0			0
$893$	3.44832e11	−	3.44832e11i	0.542252	−	0.542252i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	5.28201e9	+	5.28201e9i	0.00815886	+	0.00815886i
$898$		0			0
$899$		−	6.37451e11i		−	0.975907i
$900$		0			0
$901$	3.11202e11			0.472219
$902$		0			0
$903$	2.26397e11	−	2.26397e11i	0.340502	−	0.340502i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−8.63081e11	−	8.63081e11i	−1.27533	−	1.27533i	−0.943252	−	0.332077i	$-0.892251\pi$
$907$	−8.63081e11	−	8.63081e11i	−1.27533	−	1.27533i	−0.332077	−	0.943252i	$-0.607749\pi$
$908$		0			0
$909$			5.71282e11i			0.836749i
$910$		0			0
$911$	−6.07073e11			−0.881388			−0.440694	−	0.897657i	$-0.645268\pi$
$911$	−6.07073e11			−0.881388			−0.440694	+	0.897657i	$0.645268\pi$
$912$		0			0
$913$	7.95641e10	−	7.95641e10i	0.114508	−	0.114508i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	4.47455e11	+	4.47455e11i	0.632808	+	0.632808i
$918$		0			0
$919$			7.53310e11i			1.05612i	0.849208	+	0.528058i	$0.177080\pi$
$919$			7.53310e11i			1.05612i	−0.849208	+	0.528058i	$0.822920\pi$
$920$		0			0
$921$	2.34081e10			0.0325333
$922$		0			0
$923$	6.10412e10	−	6.10412e10i	0.0841039	−	0.0841039i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	6.74626e10	+	6.74626e10i	0.0913574	+	0.0913574i
$928$		0			0
$929$			1.02252e12i			1.37281i	0.727220	+	0.686405i	$0.240812\pi$
$929$			1.02252e12i			1.37281i	−0.727220	+	0.686405i	$0.759188\pi$
$930$		0			0
$931$	9.49804e11			1.26426
$932$		0			0
$933$	−9.24528e10	+	9.24528e10i	−0.122009	+	0.122009i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−8.30632e10	−	8.30632e10i	−0.107758	−	0.107758i	0.651172	−	0.758930i	$-0.274278\pi$
$937$	−8.30632e10	−	8.30632e10i	−0.107758	−	0.107758i	−0.758930	+	0.651172i	$0.774278\pi$
$938$		0			0
$939$		−	1.63779e11i		−	0.210667i
$940$		0			0
$941$	−1.53102e11			−0.195264			−0.0976318	−	0.995223i	$-0.531127\pi$
$941$	−1.53102e11			−0.195264			−0.0976318	+	0.995223i	$0.531127\pi$
$942$		0			0
$943$	5.44661e11	−	5.44661e11i	0.688779	−	0.688779i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−3.34420e11	−	3.34420e11i	−0.415807	−	0.415807i	0.467948	−	0.883756i	$-0.344993\pi$
$947$	−3.34420e11	−	3.34420e11i	−0.415807	−	0.415807i	−0.883756	+	0.467948i	$0.844993\pi$
$948$		0			0
$949$		−	1.16679e11i		−	0.143856i
$950$		0			0
$951$	2.00233e10			0.0244801
$952$		0			0
$953$	2.54367e11	−	2.54367e11i	0.308382	−	0.308382i	−0.535900	−	0.844282i	$-0.680027\pi$
$953$	2.54367e11	−	2.54367e11i	0.308382	−	0.308382i	0.844282	+	0.535900i	$0.180027\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	9.37551e10	+	9.37551e10i	0.111776	+	0.111776i
$958$		0			0
$959$			1.26566e12i			1.49639i
$960$		0			0
$961$	−3.98177e11			−0.466856
$962$		0			0
$963$	−7.53124e10	+	7.53124e10i	−0.0875712	+	0.0875712i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	8.49174e11	+	8.49174e11i	0.971159	+	0.971159i	0.999596	−	0.0284361i	$-0.00905273\pi$
$967$	8.49174e11	+	8.49174e11i	0.971159	+	0.971159i	−0.0284361	+	0.999596i	$0.509053\pi$
$968$		0			0
$969$			1.05601e11i			0.119777i
$970$		0			0
$971$	−1.46271e12			−1.64544			−0.822720	−	0.568448i	$-0.807544\pi$
$971$	−1.46271e12			−1.64544			−0.822720	+	0.568448i	$0.807544\pi$
$972$		0			0
$973$	−8.04545e11	+	8.04545e11i	−0.897633	+	0.897633i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	8.89887e11	+	8.89887e11i	0.976690	+	0.976690i	0.999734	−	0.0230445i	$-0.00733594\pi$
$977$	8.89887e11	+	8.89887e11i	0.976690	+	0.976690i	−0.0230445	+	0.999734i	$0.507336\pi$
$978$		0			0
$979$		−	7.81011e11i		−	0.850211i
$980$		0			0
$981$	1.11895e12			1.20819
$982$		0			0
$983$	9.53538e11	−	9.53538e11i	1.02123	−	1.02123i	0.0214616	−	0.999770i	$-0.493168\pi$
$983$	9.53538e11	−	9.53538e11i	1.02123	−	1.02123i	0.999770	−	0.0214616i	$-0.00683196\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	1.97315e11	+	1.97315e11i	0.207917	+	0.207917i
$988$		0			0
$989$		−	1.01552e12i		−	1.06146i
$990$		0			0
$991$	1.35907e12			1.40912			0.704561	−	0.709643i	$-0.251144\pi$
$991$	1.35907e12			1.40912			0.704561	+	0.709643i	$0.251144\pi$
$992$		0			0
$993$	−6.55195e10	+	6.55195e10i	−0.0673866	+	0.0673866i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−3.95894e11	−	3.95894e11i	−0.400680	−	0.400680i	0.477793	−	0.878473i	$-0.341437\pi$
$997$	−3.95894e11	−	3.95894e11i	−0.400680	−	0.400680i	−0.878473	+	0.477793i	$0.841437\pi$
$998$		0			0
$999$		−	3.61868e11i		−	0.363319i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.9.f.c.57.3	✓	12
5.2	odd	4	inner	100.9.f.c.93.4	yes	12
5.3	odd	4	inner	100.9.f.c.93.3	yes	12
5.4	even	2	inner	100.9.f.c.57.4	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.9.f.c.57.3	✓	12	1.1	even	1	trivial
100.9.f.c.57.4	yes	12	5.4	even	2	inner
100.9.f.c.93.3	yes	12	5.3	odd	4	inner
100.9.f.c.93.4	yes	12	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	100.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-11.9100 + 11.9100i) q^{3} +(-2673.78 - 2673.78i) q^{7} +6277.30i q^{9} -8327.31 q^{11} +(1552.39 - 1552.39i) q^{13} +(39830.2 + 39830.2i) q^{17} -111305. i q^{19} +63689.3 q^{21} +(142842. - 142842. i) q^{23} +(-152904. - 152904. i) q^{27} +945318. i q^{29} -674325. q^{31} +(99178.3 - 99178.3i) q^{33} +(1.18332e6 + 1.18332e6i) q^{37} +36977.9i q^{39} +3.81303e6 q^{41} +(3.55470e6 - 3.55470e6i) q^{43} +(3.09808e6 + 3.09808e6i) q^{47} +8.53335e6i q^{49} -948755. q^{51} +(3.90661e6 - 3.90661e6i) q^{53} +(1.32564e6 + 1.32564e6i) q^{57} +2.24160e7i q^{59} -5.70972e6 q^{61} +(1.67841e7 - 1.67841e7i) q^{63} +(1.68179e7 + 1.68179e7i) q^{67} +3.40250e6i q^{69} +3.93208e7 q^{71} +(3.75805e7 - 3.75805e7i) q^{73} +(2.22654e7 + 2.22654e7i) q^{77} +2.25314e7i q^{79} -3.75432e7 q^{81} +(-9.55460e6 + 9.55460e6i) q^{83} +(-1.12587e7 - 1.12587e7i) q^{87} +9.37891e7i q^{89} -8.30148e6 q^{91} +(8.03121e6 - 8.03121e6i) q^{93} +(-1.82973e7 - 1.82973e7i) q^{97} -5.22731e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 420 q^{11} - 921168 q^{21} + 3833112 q^{31} + 3587532 q^{41} + 46092564 q^{51} + 31354704 q^{61} - 29589384 q^{71} + 104018868 q^{81} + 433229088 q^{91}+O(q^{100}) \) 12 * q - 420 * q^11 - 921168 * q^21 + 3833112 * q^31 + 3587532 * q^41 + 46092564 * q^51 + 31354704 * q^61 - 29589384 * q^71 + 104018868 * q^81 + 433229088 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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